\begin{align*}
  \G_\kk(\E)&=\big[(\E+\im\eta)\SO_\kk - \HH_\kk - \sum_\idxE\SE_{\idxE,\kk}(\E-\mu_\idxE)\big]^{-1}
  \\
  \Scat_{\idxE,\kk}(\E) &=i\big(\SE_{\idxE,\kk}(\E-\mu_\idxE)-\SE^\dagger_{\idxE,\kk}(\E-\mu_\idxE)\big)
  \\
  \Spec_{\idxE,\kk}(\E) &=\G_\kk(\E)\Scat_{\idxE,\kk}(\E)\G_\kk^\dagger(\E)
  % \\
  % \DM & =\frac1{2\pi}
  % \iint_\BZ\dEBZ\cd \kk \dd\E\, \sum_\idxE\Spec_{\idxE,\kk}(\E) n_{F,\idxE}(\E)
  % \eikr,
\end{align*}